Exported textures are black
ok so I think I know exactly what's your problem if you are using cycles to paint your UV maps all you have to do is 
- create an image texture in the UV image editor give it a name.
- go to the node editor and create an image texture node.
- select your texture with the left mouse button make sure that it's highlighted in orange color.


now when you paint it will show up on the UV map and when you exported it hopefully it won't be black


ps: if this didn't solve it pls post a snap of your setup